Multiscale Gossip for Efficient Decentralized Averaging in Wireless Packet Networks
Abstract
This paper describes and analyzes a hierarchical gossip algorithm for solving the distributed average consensus problem in wireless sensor networks. The network is recursively partitioned into subnetworks. Initially, nodes at the finest scale gossip to compute local averages. Then, using geographic routing to enable gossip between nodes that are not directly connected, these local averages are progressively fused up the hierarchy until the global average is computed. We show that the proposed hierarchical scheme with $k$ levels of hierarchy is competitive with stateoftheart randomized gossip algorithms, in terms of message complexity, achieving $\epsilon$accuracy with high probability after $O\big(n \log \log n \log \frac{kn}{\epsilon} \big)$ messages. Key to our analysis is the way in which the network is recursively partitioned. We find that the optimal scaling law is achieved when subnetworks at scale $j$ contain $O(n^{(2/3)^j})$ nodes; then the message complexity at any individual scale is $O(n \log \frac{kn}{\epsilon})$, and the total number of scales in the hierarchy grows slowly, as $\Theta(\log \log n)$. Another important consequence of hierarchical construction is that the longest distance over which messages are exchanged is $O(n^{1/3})$ hops (at the highest scale), and most messages (at lower scales) travel shorter distances. In networks that use linklevel acknowledgements, this results in less congestion and resource usage by reducing message retransmissions. Simulations illustrate that the proposed scheme is more messageefficient than existing stateoftheart randomized gossip algorithms based on averaging along paths.
 Publication:

arXiv eprints
 Pub Date:
 November 2010
 DOI:
 10.48550/arXiv.1011.2235
 arXiv:
 arXiv:1011.2235
 Bibcode:
 2010arXiv1011.2235T
 Keywords:

 Computer Science  Distributed;
 Parallel;
 and Cluster Computing
 EPrint:
 (under Review)